Best Answer

An example is given here:

Any set that is easy to think of will be a Borel set, so an example of a non-Borel set will be complicated.

Another approach: All Borel sets are Lebesgue measurable. The axiom of choice can be used to give an example of a non-measurable set, and this set will also be a non-Borel set.


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โˆ™ 2009-03-30 07:02:19
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Q: Give an example of a subset of R that is not a Borel set?
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Related questions

What is an example of a simple borel measurable function?

Characteristic function of any borel set is an example of simple Borel function

Can any set be a proper subset of itself give an example of why or why not?

No, by definition. A proper subset is a subset that contains some BUT NOT ALL elements of the original set.

What is a subset in maths?

A set "A" is said to be a subset of of set "B", if every element in set "A" is also an element of set "B". If "A" is a subset of "B" and the sets are not equal, "A" is said to be a proper subset of "B". For example: the set of natural numbers is a subset of itself. The set of square numbers is a subset (and also a proper subset) of the set of natural numbers.

What is the Subset?

A subset is a smaller set that is part of a larger set. For example, the set of animals contains the subset of reptiles, the subset of mammals, and various others. Or in mathematics, the set of real numbers contains the subset of positive integers, the subset of negative integers, the subset of rational numbers, etc.

Can a subset of infinite set be infinite?

Yes. For example, the set of odd natural numbers is a infinite subset of the set of integers.

An example of why any subset can not be a proper subset?

Assume that set A is a subset of set B. If sets A and B are equal (they contain the same elements), then A is NOT a proper subset of B, otherwise, it is.

What is example of subset in math?

The set of Rational Numbers is a [proper] subset of Real Numbers.

What is a subset in mathematics?

If all elements in set "A" are also elements of set "B", then set "A" is a subset of set "B". If the sets are not equal (set "B" also has some elements that are not in set "A"), then set "A" is a PROPER subset of set "B".Answer:In simple words: a subset is a set (a group) that is within another set. For example, the set of odd integers (odd numbers) is a subset of the set of all integers.A non-math example: the set of urbanites is a subset of the set of all people.See the first Answer (above) for more detail.

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An improper subset is identical to the set of which it is a subset. For example: Set A: {1, 2, 3, 4, 5} Set B: {1, 2, 3, 4, 5} Set B is an improper subset of Set Aand vice versa.

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If you have a set S, the only improper subset of S is S itself. An improper subset contains all elements of S and no others. It is therefore equivalent to S. For example if S ={1,2,3} then the improper subset is {1,2,3}, and an example proper subset is {1,2}.

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